Question

$1.0g$ of a sample containing $NaCl$ , $KCl$ and some other impurity is dissolved in excess of water and treated with excess of $AgN{O_3}$ solution. A $2.0g$ precipitate of $AgCl$ separates out the sample is $23\%$ by mass in sodium. Determine the mass percentage of $KCl$ in the sample.
A) $45\%$
B) $29.28\%$
C) $10\%$
D) $52.10\%$

Answer 1

Here we need to determine the mass percentage. Mass percent of an element in a compound can be calculated by dividing mass of element in one mole of a compound by compound molar mass. Then it can be multiplied by $100$. Actually the mass percent formula is expressed as solving to get the molar mass of every element in one mole of a compound.

Complete step-by-step answer:
Here the mass of sample given is $1.0g$
The percentage of sample by mass in sodium is $23\%$
Mass of sodium here can be calculated as $\dfrac{{23}}{{100}} \times 1.0 = 0.23g$
Here atomic masses of $Na$ and $Cl$ are $23.0g/mol$ and $35.5g/mol$ respectively.
When we take the case of $NaCl$ , $0.23g$ of $Na$ can be corresponded to $\dfrac{{35.5}}{{23.0}} \times 0.23 = 0.355g$ of chlorine.
We know the molar mass of $AgCl$ is $143.5g/mol$ and that the atomic mass of $Cl$ is $35.5g/mol$ .
2.0g$$$$AgCl of $AgCl$ precipitate is separated out as given in the question.
Therefore here $2.0g$ of $AgCl$ thus corresponds to $\dfrac{{35.5}}{{143.5}} \times 2.0 = 0.495$ grams of chlorine.
Out of the total $0.495g$ of chlorine $0.355g$ of chlorine is from $NaCl$.
Therefore the remaining that is , $0.495 - 0.355 = 0.140$gram is from $KCl$ .
We know the molar mass of $KCl$ is $74.6g/mol$.
Atomic mass of chlorine is $35.5g/mol$
Then $0.140g$ of chlorine corresponds to $\dfrac{{74.6}}{{35.5}} \times 0.140 = 0.2928g$ of $KCl$.
The mass of the sample is $1.0g$ as given in question. The mass of $KCl$ is $0.2928g$ as calculated above.
Therefore mass percent of $KCl$ in sample can be calculated as the following,
$\dfrac{{0.2928}}{{1.0}} \times 100 = 29.28\%$

Hence option B is the correct answer.
Note: Mass percent is a way of expressing degree. More than that , it describes components involved in a particular mixture. The solution composition is actually described in mass percentage. It deals with showing mass of solute which is present during a given mass of solution. Here the number of moles is expressed in mass percent by moles.